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 (22) Longitudinal Mass and Transverse Mass. We find under these conditions that the force of inertia is proportional to the acceleration with a coefficient of proportionality analogous to mass, but which is here a function of the velocity, and increases indefinitely, like the kinetic energy, as the velocity tends to approach that of light. Moreover, this electromagnetic mass differs for the same velocity, according as the acceleration is parallel or perpendicular to the direction of the velocity. There is, corresponding to the direction, a longitudinal and a transverse mass. Mass is then no longer a scalar quantity, but has the symmetry of a tensor parallel to the velocity. No experimental fact yet allows us to verify this dissymmetry of the mass of the electrons, which becomes evident only when the velocity is of the same order as that of light, but the variation of the transverse mass with the velocity has been proven by Kaufmann for the β rays of radium, which consist of particles identical with the cathode rays. It is sufficient to compare the deviations of these rays in the electric and magnetic fields perpendicular to their direction in order to deduce, by application of the equations of the dynamics of the electron, their velocity and the ratio of the charge to the transverse mass of the particles which compose them. This ratio decreases as the velocity increases, and, if we consider as fundamental the principle of the conservation of electricity, we conclude from it an actual increase of the transverse mass according to a law easy to compare with that which the theory gives for the electromagnetic mass.

(23) Matter of the Philosophers. But before discussing the result of this comparison, I wish to point out a logical difficulty raised by the course which we have followed: we are accustomed to consider as fundamental the ideas of mass and force, built up in order to represent the laws of motion of matter; we, a priori, conceive of mass as a perfectly invariable scalar quantity.

Now, let us suppose the possibility of a material representation of the ether: we apply to it the equations of material dynamics, and we are led to admit for the electrons, which form a part of matter, and consequently for matter itself, a dissymmetrical mass, tensorial and variable.

To what, then, should the equations of ordinary dynamics apply, and what are the ideas considered as fundamental which they imply? To an abstract matter, the matter of the philosophers, which could not be ordinary matter, since it is inseparable from electric charges, and which is probably made up of an agglomeration of electrons in periodic motion, stable under their mutual actions? Or to the ether? But we have no idea of what can be its mass or motion.

It is, indeed, rather the ether which it is necessary to consider as fundamental, and it is then natural to define it initially by those properties